Summary of the Lesson
The lesson I am teaching is focused on factoring with quadratics and square roots (radicals). This is one of the last concepts we cover in Algebra I before administering the End of Course Examination. The methods I traditionally use to teach this lesson evolve over a period of weeks as we cover prerequisite skills for factoring (factor trees, greatest common factors, perfect squares, properties of exponents, and scientific notation). My traditional assessments for this unit are daily warm ups to check understanding along the way and then quizzes and a unit test. As for planning an open-ended student assignment, I think in preparing for the coming school year, I will present the rules, laws, and theorems to my students as normal. Then, they will be responsible for creating an electronic presentation and/or poster quality displays to demonstrate their understanding of these varied concepts. This unit typically takes three weeks to master, so their assignments will be tiered from day-to-day and week-to-week. At the culmination of the unit, I will be able to use the rubric I have created to measure their total understanding as well as their mastery of the various topics surrounding factoring.
Standards Addressed in the Lesson
Carry out a procedure to factor binomials, trinomials, and polynomials by using various techniques (including the greatest common factor, the difference between two squares, and quadratic trinomials).
Carry out a procedure to solve quadratic equations by factoring.
Judge the reasonableness of mathematical solutions.
Apply the laws of exponents and roots to solve problems.
Objectives of the Lesson
Students will be able to use the distributive property to factor a polynomial and solve polynomial equations by factoring.
Students will be able to simplify polynomial expressions by adding and subtracting, and by factoring in a variety of ways. Students will also be able to FOIL and solve equations by factoring.
The students will be able to use properties of radicals to simplify radicals.
Student Artifacts from the Lesson
These quizzes are samples from students in Algebra I during the 2010-2011 school year. I do not have samples of the open-ended assessmentto include since we are on break. One quiz sample is the material prior to factoring (it is FOIL and distributive property) and the other quiz sample is scientific notation, simplifying radicals, and finding roots (factoring) quadratics.Students have to check their work to ensure the solution(s) found are reasonable.
Scored Rubrics for three Students
The rubric I plan to use during the coming school year is attached. I am unable to assess student work at this time due to being on break.
How did this assessment tool compare with a standardized test?
In reflecting on my use of traditional and authentic assessments with my students, I feel that it is important for me to employ both in my classroom to meet the needs of my diverse students. I teach in a school that is mainly impoverished students who live in single-parent or non-traditional homes. I am not sure these people have the means to provide materials necessary to create projects or support systems in the home to see that it is carried out. The best method for me to ensure success would be to provide materials and class time for these students to complete their work. This would also ensure proper guidance and oversight from an adult (me) to make sure they follow instructions and thoroughly complete their assignments. I do think this project would offer differentiated instruction in my classroom and provide all learners with an option for mastery of the concepts.
What did you learn by the experience?
Every year that I teach, I become more humble and more open-minded about my views and feelings towards the school and classroom. I have seen a vast array of poverty levels in my classroom as well as struggling parents who cannot compete with those of means. There are times I get discouraged by these economic barriers and worry about how I can make a difference in these children’s lives. By me composing and creating authentic assessments that provide alternatives to traditional ones, I afford my students an opportunity to explore their own creativity and become more global learners. I am excited about the coming school year and plan to implement this project within all of my Algebra I classes.
Summary of the Lesson
The lesson I am teaching is focused on factoring with quadratics and square roots (radicals). This is one of the last concepts we cover in Algebra I before administering the End of Course Examination. The methods I traditionally use to teach this lesson evolve over a period of weeks as we cover prerequisite skills for factoring (factor trees, greatest common factors, perfect squares, properties of exponents, and scientific notation). My traditional assessments for this unit are daily warm ups to check understanding along the way and then quizzes and a unit test. As for planning an open-ended student assignment, I think in preparing for the coming school year, I will present the rules, laws, and theorems to my students as normal. Then, they will be responsible for creating an electronic presentation and/or poster quality displays to demonstrate their understanding of these varied concepts. This unit typically takes three weeks to master, so their assignments will be tiered from day-to-day and week-to-week. At the culmination of the unit, I will be able to use the rubric I have created to measure their total understanding as well as their mastery of the various topics surrounding factoring.
Standards Addressed in the Lesson
Objectives of the Lesson
Student Artifacts from the Lesson
These quizzes are samples from students in Algebra I during the 2010-2011 school year. I do not have samples of the open-ended assessmentto include since we are on break. One quiz sample is the material prior to factoring (it is FOIL and distributive property) and the other quiz sample is scientific notation, simplifying radicals, and finding roots (factoring) quadratics.Students have to check their work to ensure the solution(s) found are reasonable.
Scored Rubrics for three Students
The rubric I plan to use during the coming school year is attached. I am unable to assess student work at this time due to being on break.
Reflections on the Assignment
- How did this assessment tool compare with a standardized test?
In reflecting on my use of traditional and authentic assessments with my students, I feel that it is important for me to employ both in my classroom to meet the needs of my diverse students. I teach in a school that is mainly impoverished students who live in single-parent or non-traditional homes. I am not sure these people have the means to provide materials necessary to create projects or support systems in the home to see that it is carried out. The best method for me to ensure success would be to provide materials and class time for these students to complete their work. This would also ensure proper guidance and oversight from an adult (me) to make sure they follow instructions and thoroughly complete their assignments. I do think this project would offer differentiated instruction in my classroom and provide all learners with an option for mastery of the concepts.- What did you learn by the experience?
Every year that I teach, I become more humble and more open-minded about my views and feelings towards the school and classroom. I have seen a vast array of poverty levels in my classroom as well as struggling parents who cannot compete with those of means. There are times I get discouraged by these economic barriers and worry about how I can make a difference in these children’s lives. By me composing and creating authentic assessments that provide alternatives to traditional ones, I afford my students an opportunity to explore their own creativity and become more global learners. I am excited about the coming school year and plan to implement this project within all of my Algebra I classes.